Analysis, Control and Circuit Implementation of a Novel 4D Chaotic System

Abstract

本文首先对新四维混沌系统的动力学特性进行分析。而后，采用改进型模块化混沌电路设计方法设计新四维混沌系统的电路模型并于A + D Lab实验平台上搭建其模拟电路实现，从硬件上验证该新四维混沌系统可产生混沌运动现象。针对新四维混沌系统的稳定性控制，本文通过建立被控新四维混沌系统的数学模型，基于Lyapunov稳定性理论，设计单变量线性反馈控制器并搭建其硬件电路实现，从硬件上验证被控新四维混沌系统不再产生混沌或周期运动而是渐近稳定于平衡点原点，以及所设计的线性反馈控制器的可行性与有效性。 The dynamics of the novel four-dimensional (4D) chaotic system are presented. The analog circuit is derived from the modified module-based approach to chaotic circuit design and implemented by means of the A + D Lab platform to illustrate that the novel 4D chaotic system could generate chaos on hardware. For chaos control of the novel 4D chaotic system, the mathematical model of the controlled system is formulated, and a linear feedback controller only with one variable is designed based on the Lyapunov stability theory and implemented by circuit. The output signals of the circuit implementation show that the state variables of the controlled novel 4D chaotic system are no longer chaotic or periodic but asymptotically converge to zero, which indicates that the controlled system is asymptotically stable at the origin and the linear feedback controller is feasible and effective.